In a statement issued by the department, State Secretary Mike Pompeo accused Iran of engaging in "an escalating of threatening actions and statements in recent weeks". "They both provided assurances that they understood that was their responsibility".
Mrs May reportedly gave the green light to the company bidding for work on "non-core" aspects of the hi-tech 5G network at the NSC meeting, overruling concerns from ministers including Gavin Williamson, who was later sacked as defence secretary over suspicions that he had leaked details of discussions. "In each of those meetings, those two leaders promised that that was their objective, too, they were moving towards that goal", he said.
As tensions rise between Washington and Tehran, Baghdad in some ways is caught in the middle.
Pompeo said he expressed USA support for Iraqi sovereignty, noting: "We don't want anyone interfering in their country, certainly not by attacking another nation inside of Iraq".
The visit comes two days after the USA announced it was dispatching an aircraft carrier strike group and bomber task force to the Middle East to send a "clear and unmistakeable" message to Iran.
The "campaign to continue to prevent ISIS terror inside of Iraq itself is something that's very central ... to the Iraqi government", Pompeo said.
Iran, meanwhile, was expected to announced Wednesday that it would partially withdraw from the nuclear deal it struck with world powers in 2015.
But in response to a question about threats from Iran or its proxies on USA forces in Iraq, the top U.S. diplomat mentioned both Iraq and Jordan.
In Iraq, a debate has been raging in recent months over the fate of some 5,200 United States troops stationed across the country.
On Tuesday, instead of flying to Germany, Pompeo made an unannounced detour to Iraq - where Iran has a major influence - and said that the country's leaders had promised to protect United States interests.
But Iraq is also tightly enmeshed with Iran in trade, security and political matters, and it has been loath to antagonize its larger neighbour.
Mr Trump previous year unilaterally pulled the U.S. out of an global nuclear deal with Iran, but the United Kingdom and other European powers have refused to follow his lead. "This is an obligation that Iraq honours", he said. The U.S. also designated Iran's Revolutionary Guard as a terrorist group, the first ever for an entire division of another government.
President Hassan Rouhani Wednesday announced Tehran's withdrawal from complying with the restrictions posed by the Iran nuclear deal on the country's enriched uranium reserves and heavy water supplies.